1.This dissertion mainly study the Erlang(2) risk model with constant interest force, we consider some important distributions and rusults: the non-ruin probability, the surplus immediately before ruin, the deficit at ruin, the joint distribution of the surplus immediately before ruin and the deficit at ruin, the expected discounted penalty at ruin and so on.
本学位论文主要研究常利率下的Erlang(2)风险模型。 讨论了不破产概率，破产前瞬间盈余分布，破产时赤字分布，破产前盈余和破产时赤字的联合分布以及罚金折现期望等几个重要的量。
2.In chapter one, we introduce the Erlang(2) risk process with constant interest force and give the definition of the probability of ruin, the surplus immediately before ruin, the deficit at ruin, the joint distribution of the surplus immediately before ruin and the deficit at ruin, the expected discounted penalty at ruin respectively.
在第一章引言部分，引入所要讨论的常利率环境下的Erlang(2)风险模型，定义了破产概率，破产前瞬间盈余分布，破产时赤字分布，破产前盈余和破产时赤字的联合分布以及罚金折现期望。
3.In this paper,we discuss a compound renewal risk model with premium arrival by equilibrium renewal process,then we get the live probability in finite time t,the joint distribution of the time of ruin T and the asset surplus U(T) at ruin,and the joint distribution of the time of ruin T and the surplus immediately before ruin U(T ).
本文研究保费到达为平衡更新过程的复合更新风险模型 ,给出了有限时间内的生存概率分布 ,破产时间 T与破产时资产盈余 U(T)的联合分布 ,及破产时间 T与破产前瞬时盈余 U(T- )的联合分布 .
4.Under the discrete time risk model with constant interest, SUN Li-juan and GU Lan (2002) have discussed some ruin problems which are about the distributions of the surplus immediately before ruin and the time of the severity of ruin.
孙立娟、顾岚(2002)则在具有常利息率的离散时间模型下，讨论了破产前盈余分布、破产持续时间分布的问题。
5.In chapter one, we introduce the Erlang(2) risk process perturbed by diffusion and give the definition of the time at ruin, the surplus immediately before ruin, the dificit at ruin.
C(u,x)=1/2 integral from n=0 to +∞[G(2u+ct,x)+G(ct,x)]e~(-λt)(1+λt)h(u/σ,t)dt
6.This dissertation is devoted to dealing with the ruin theory for some kinds of risk models which include the ruin problem for a correlated aggregate claims model with Poisson and Erlang(2) risk processes, the ruin theory for a discrete-time risk model with dependence between claim sizes and the occurrence of claim and for the risk process perturbed by diffusion in a Markovian environment.
本文致力于研究几种不同风险模型的破产理论,主要考虑了常利率下总索赔额为Poisson和Erlang(2)相关的风险模型及索赔量与索赔发生的概率相依的离散风险模型的破产问题,最后带干扰的马氏环境下的一类风险模型的破产问题也得到研究。
7.On the condition that police arrival and insurance indemnity follow Cox process,we establish a double Cox risk model with additional premium and obtain the upper bound of ruin probability. Furthermore,under the assumption that police arrival and insurance indemnity follow process with the same accumulate intension,we provide an explicit expression of the ruin probability formula.
在保费到达和理赔的发生都服从Cox 过程的情形下,建立了带附加保费的双Cox 风险破产模型,得到了破产概率上界并在假设保单的到达和理赔的发生具有相同的累积强度过程时,给出了破产概率的明确表达式。
8.Sparre Andersen (1957) considered the situation in which claims occur as a general renewal process, and an explicit result for the ultimate ruin probability was derived for a particular case. The explicit expression for Laplace transform of the ruin time with exponentially claim amount distribution is obtained by Malinovskii (1998); and Wang and Liu (2002) generalized the result to the case when claim amount has the mixed distribution of two exponentials.
Sparre Andersen(1957)研究了当索赔发生为更新过程时的情况,并得到某些情况下的最终破产概率,在此模型下,Malinovskii(1998)得到了索赔额为指数分布时的破产概率的拉氏变换,Wang and Liu(2002)把这一结果推广到索赔额为混和指数分布时的情况。
9.Gambling was his ruin[the ruin of him
赌博是他堕落的原因。
10.Sparre Andersen considered the situation in which claims occur as a general renewal process in 1957, then he constructed the renewal risk model and began to study ruin probability. Since then, the calculation of ruin probability became increasingly important. See, [2] [3] [4] [15] for details.
由于经典风险模型中索赔发生总服从Poisson过程的假定并不完全符合保险业的实际运营情况,Sparre Andersen于1957年考虑索赔发生服从一般更新过程,从而建立更新风险模型,自此破产概率的计算成为一个中心问题,可参阅文献[2][3][4][15]等。
